Let p(x) be a function defined on R such that `p '(x)""=""p '(1-x)` , for all `x in [0,""1],""p(0)""=""1` and `p(1)""=""41` . Then `int_0^1p(x)dx` equals (1) 21 (2) 41 (3) 42 (4) `sqrt(41)`

Let p(x) be a function defined on R such that p'(x)=p'(1-x) for all x epsilon[0,1],p(0)=1, and p(1)=41 . Then int_(0)^(1)p(x)dx is equal to

Let p(x) be a function defined on R such that lim_(xrarr infty) f (3x)/(f(x))=1,p'(x)=p'(1-x),"for all" x in [0,1],p(0)=1 and p(1)=41."Then" , int_(0)^(1)p(x) dx equals

Let p(x) be a function defined on R such that (lim)_(x->oo)(f(3x))/(f(x))=1,\ p^(prime)(x)=p^(prime)(1-x),\ for\ a l l\ x in [0,\ 1],\ p(0)=\ 1a n d\ p(1)=41. Then int_0^1p(x)dx equals a. sqrt(41) b. 21 c. 41 d. 42

Let P(x) be a polynomial of degree 11 such that P(x) = (1)/(x + 1) for x = 0, 1, 2, 3,"…."11 . The value of P(12) is.

Let P(x) be a polynomial of degree 11 such that P(x)=(1)/(x+1), for x=0,1,2,...11. The value of P(12) is

P(x) is a non-zero polynomial such that P(0)=0 and P(x^(3))=x^(4)P(x).P'(1)=7 and int_(0)^(1)P(x)=1.5 then int_(0)^(1)P(x)P'(x)dx=

Let P be a non-zero polynomial such that P(1+x)=P(1-x) for all real x, and P(1)=0. Let m be the largest integer such that (x-1)^m divides P(x) for all such P(x). Then m equals